Abstract: In this paper, we study the input impedance characteristics of axial mode helical antennas to find an effective way for matching it to 50 Ω. The study is done on the important matching parameters such as like wire diameter and helix to the ground plane gap. It is intended that these parameters control the matching without detrimentally affecting the radiation pattern. Using transmission line theory, a simple broadband technique is proposed, which is applicable for perfect matching of antennas with similar design parameters. We provide design curves to help to choose the proper dimensions of the matching section based on the antenna’s unmatched input impedance. Finally, using the proposed technique, a 4-turn axial mode helix is designed at 2.5 GHz center frequency and the measurement results of the manufactured antenna will be included. This parametric study gives a good insight into the input impedance characteristics of axial mode helical antennas and the proposed impedance matching approach provides a simple, useful method for matching these types of antennas.
Abstract: A uniquely restricted matching is defined to be a
matching M whose matched vertices induces a sub-graph which has
only one perfect matching. In this paper, we make progress on the
open question of the status of this problem on interval graphs (graphs
obtained as the intersection graph of intervals on a line). We give
an algorithm to compute maximum cardinality uniquely restricted
matchings on certain sub-classes of interval graphs. We consider two
sub-classes of interval graphs, the former contained in the latter, and
give O(|E|^2) time algorithms for both of them. It is to be noted that
both sub-classes are incomparable to proper interval graphs (graphs
obtained as the intersection graph of intervals in which no interval
completely contains another interval), on which the problem can be
solved in polynomial time.
Abstract: Graph decompositions are vital in the study of
combinatorial design theory. A decomposition of a graph G is a
partition of its edge set. An n-sun graph is a cycle Cn with an edge
terminating in a vertex of degree one attached to each vertex. In this
paper, we define n-sun decomposition of some even order graphs
with a perfect matching. We have proved that the complete graph
K2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have
n-sun decompositions. A labeling scheme is used to construct the n-suns.
Abstract: Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.